Building curves: hyperbola

The hyperbola is the locus of points P of the plane such that is constant the module of the difference ld1 - d2l of the distances d1 and d2, respectively, from P to two fixed points F1 and F2, called foci of the hyperbola.

 

Moving the points F1 and F2 you adjust the foci of the hyperbola;

Moving the point A you adjust the opening of hyperbola;

Click the right mouse button on the point P and click on "Trace On";

Move the point B to plot the hyperbole.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Created with GeoGebra

 

Step-by-step construction:


Mark two points F1 and F2.

Mark a point A such that the distance F1A is less than the distance F1F2.

Make a circle c1 with center in F1 and radius F1A.

Mark on the circle c1 a point B.

Trace the line r through F1 and B.

Trace the segment BF2 and its midpoint M.

Trace the line s perpendicular to segment BF2 and through M.

P is the intersection of line r with the line s.

Cliking in "Play", you can fallow the step-by-step construction.

 

In the space below, you can make your construction of hyperbola.

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Creative Commons License
Building curves: hyperbola by MDMat is licensed under the Creative Commons Atribuição-Uso Não-Comercial-Compartilhamento pela mesma Licença 3.0 Brasil License.